Complex Heat Capacity as a Witness of Spatio-Temporal Entanglement

TL;DR

This paper introduces a thermodynamic method using complex heat capacity to detect and characterize temporal quantum entanglement in condensed-matter systems, linking measurable quantities to quantum correlations.

Contribution

It establishes a novel connection between complex heat capacity and the pseudo-density matrix formalism, enabling detection of temporal entanglement without complex state manipulations.

Findings

Complex heat capacity's imaginary part signals temporal quantum entanglement.

Analytical demonstration for a qubit-bath system shows non-classical correlations.

Bounds on imaginary heat capacity provide experimentally accessible entanglement criteria.

Abstract

We propose a novel witness of temporal quantum entanglement using the imaginary component of the complex heat capacity - a measurable thermodynamic quantity in temperature-modulated calorimetry. By establishing a direct correspondence between complex heat capacity and the pseudo-density matrix formalism, our approach enables the characterisation of both spatial and temporal quantum correlations without demanding additional state-level manipulation beyond initial tomography. We analytically demonstrate this connection for an open quantum system modelled by a qubit coupled to a thermal bath, and show how both pseudo-density matrix negativity and violations of a temporal CHSH inequality emerge as indicators of non-classical temporal correlations. We further identify bounds on the imaginary heat capacity that guarantee temporal entanglement, providing an experimentally accessible criterion at the macroscopic scale. This framework offers a feasible route for probing temporal quantum effects in condensed-matter systems and opens a viable path toward experimental realisation.